Timeline for Abstract definition of conjugate points
Current License: CC BY-SA 3.0
26 events
| when toggle format | what | by | license | comment | |
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| Nov 16 at 13:02 | comment | added | Croqueta | Your definition is wrong, which leads to the misleading comments and answers given. The conjugate points are the critical values of exp. This is the definition given in Natario's book ("Riemannian geometry with applications to mechanics and relativity"). Your question is answered in chapter 10 ("Jacobi fields") of Lee's book on Riemannian manifolds. | |
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| Dec 11, 2017 at 8:32 | history | tweeted | twitter.com/StackPhysics/status/940137189488422917 | ||
| Dec 9, 2017 at 21:38 | answer | added | Erik Jörgenfelt | timeline score: 0 | |
| Dec 9, 2017 at 21:03 | comment | added | Valter Moretti | All that is a direct application of the theorem of regular values. | |
| Dec 9, 2017 at 20:57 | comment | added | Valter Moretti | Different such pairs, if exist and therefore there are converging geodesics in that case, are necessarily far from each other. | |
| Dec 9, 2017 at 20:53 | comment | added | Valter Moretti | That definition, as it stands, says nothing about the existence of converging geodesics. It only says that if $q$ is conjugated to $S$ and $\exp(t,p)=q$, then $\exp$ is a local diffeomorphism from an open neighborhood of that $(t,p)$ to an open neighborhood of $q$. However there can exist different such pairs $(t,p) \in U$ for the given conjugate value $q$. | |
| Dec 9, 2017 at 17:44 | comment | added | Ivan Burbano | Yes Riemannian Geometry with Applications to Mechanics and Relativity | |
| Dec 9, 2017 at 17:25 | comment | added | Qmechanic♦ | Is definition taken from a reference? Title? Author? Page? | |
| Dec 9, 2017 at 17:25 | history | edited | Qmechanic♦ | CC BY-SA 3.0 |
added 44 characters in body; edited tags
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| Dec 9, 2017 at 16:32 | history | asked | Ivan Burbano | CC BY-SA 3.0 |